The present invention relates to a quantum computer.
Quantum computation involves manipulation of data in the form of quantum bits or xe2x80x9cqubitsxe2x80x9d. Whereas in classical computation a bit of information is used to represent only one of two possible logical states, namely xe2x80x9c1xe2x80x9d or xe2x80x9c0xe2x80x9d, in quantum computation, a qubit can represent both logical states simultaneously as a superposition of quantum states. This property gives rise to powerful computational parallelism. Algorithms which exploit this parallelism have been developed, for example for efficiently factorising large integers. An overview of quantum computation is found xe2x80x9cQuantum Computationxe2x80x9d by David Deutsh and Artur Ekert in Physics World, pp. 47-52, March 1998 and in xe2x80x9cQuantum Computation: An Introductionxe2x80x9d by Adriano Barenco, pp. 143-183 of xe2x80x9cIntroduction to Quantum Computation and Informationxe2x80x9d ed. Hoi-Kwong Lo, Tim Spiller and Sandu Popescu (World Scientific Publishing, 1998).
In a classical computer, a bit of information is usually represented by a voltage level. Therefore, xe2x80x9c0xe2x80x9d can be represented by a relatively low voltage level, say 0 volts, and xe2x80x9c1xe2x80x9d can be characterised by a relatively high voltage level, say 5 volts.
In a quantum computer, a qubit can be represented in a number of ways, for example using left and right polarisation states of a photon, spin-up and spin-down states of an electron and ground and excited states of quantum dot. The qubit is defined by a basis consisting of two states, which are denoted |0 greater than  and |1 greater than . Thus, the state of the qubit can be represented as:
|"psgr" greater than =a|0 greater than +b|1 greater than xe2x80x83xe2x80x83(1) 
where a and b are complex number coefficients. The qubit stores information as a combination of 0 and 1 using different values of a and b. However, a measurement of the qubit will cause it to project onto the |0 greater than  or |1 greater than  state and return the result 0 or 1 accordingly. The probabilities of returning these values are |a|2 and |b|2 respectively. In this way, the system comprised of one qubit can store two binary values, 0 and 1, at the same time, although recovery of any stored information is restricted.
A system comprised of two qubits can store up to four binary values simultaneously as a result of superposition. Therefore, a system comprising a pair of qubits, labelled A and B, is defined by a basis of four states which can be written as |0 greater than A|0 greater than B, |0 greater than A|1 greater than B, |1 greater than A|0 greater than B and |1 greater than A|1 greater than B. In the same way that a single qubit can store information as superposition of |0 greater than  and |1 greater than , a pair of qubits can store information as superposition of basis states |0 greater than A|0 greater than B, |0 greater than A|1 greater than B, |1 greater than A|0 greater than B and |1 greater than A|1 greater than B. For example, the two qubits may be prepared such that:
|"psgr" greater than AB=2xe2x88x92xc2xd(|0 greater than A|0 greater than B+|0 greater than A|1 greater than B+|1 greater than A|0 greater than B+|1 greater than A|1 greater than B)xe2x80x83xe2x80x83(2) 
Thus, four binary values 00, 01, 10 and 11 are encoded simultaneously. In this case, the two qubits exist independently of one another, such that the result of a measurement qubit A is independent of the result of a measurement of qubit B.
However, if the two qubits are entangled, then the two measurements will become correlated. Entanglement allows qubits to be prepared such that:
|"psgr" greater than AB=2xe2x88x92xc2xd(|0 greater than A|0 greater than B+|1 greater than A|1 greater than B)xe2x80x83xe2x80x83(3) 
Thus, binary values 00 and 11 are encoded simultaneously. However, if qubit A is measured and a result 0 is returned, then the outcome of a subsequent measurement of qubit B will, with certainty, also be 0.
A system comprised of three qubits is defined by basis of eight states which can store eight binary numbers, 000, 001, . . . , 111 simultaneously.
In general, a system of m qubits has a basis of 2m states and can be used to represent numbers from 0 to 2mxe2x88x921. Thus, a quantum computer has a clear advantage over its classical counterpart in that it that it can store 2m numbers simultaneously, whereas a classical computer with an m-bit input register can only store one of these numbers at a time.
It is the ability to store many numbers simultaneously using superposition of quantum states which makes quantum parallel processing possible. Using a single computational step it is possible to perform the same mathematical operation on 2m different numbers at the same time and produce a superposition of corresponding output states. To achieve the same result in a classical computer, the computational step would need to be repeated 2m times or require 2m different processors.
Despite the power of quantum parallel processing, there is a drawback that only one state can be measured. However, some processes, such as sorting or searching of a database, may require only a single-valued solution. Thus, a system in which a mathematical operation has been performed on a plurality of numbers simultaneously may still benefit from parallelism provided that the desired value is the most probable outcome when the system is measured. An example of a quantum algorithm which operates in this way is described in xe2x80x9cA Fast Quantum Mechanical Algorithm for Database Searchxe2x80x9d by Lov Grover, pp. 212-219, Proceedings of the 28th Annual ACM Symposium on the Theory of Computing (Philadelphia, May 1996).
Ideally, the qubits in the quantum computer should be identical, while also being individually tuneable in energy. Several systems have been proposed which fulfil the requirements of having identical qubits which are individually controllable. For example, experimental quantum computers have been implemented using atomic beams, trapped ions and bulk nuclear magnetic resonance. Examples of these systems are described in xe2x80x9cQuantum computers, Error-Correction and Networking: Quantum Optical approachesxe2x80x9d by Thomas Pellizari, pp. 270-310 and xe2x80x9cQuantum Computation with Nuclear Magnetic Resonancexe2x80x9d by Isaac Chuang pp. 311-339 of xe2x80x9cIntroduction to Quantum Computation and Informationxe2x80x9d ibid. However, these systems are difficult to fabricate and have the added disadvantage that their architecture cannot be easily scaled-up to accommodate a large number of qubits, i.e. more than about 10 qubits.
Quantum computers may also be implemented using solid-state systems employing semiconductor nanostructures and/or Josephson junctions. One such device is described in xe2x80x9cCoherent control of macroscopic quantum states in a single-Cooper-pair boxxe2x80x9d by Y. Nakamura, Yu. A. Pashkin and J. S. Tsai, Nature, volume 398, p 786 (1999). Another device is described in our EP application 01304745.1. The advantage of such solid state systems is that they are better suited to being scaled and so provide quantum computers of practical utility. However, in semiconductor-based systems, the qubits are individually fabricated using lithographic methods. As a result, the qubits are slightly different from one another, even though they are intended to be identical.
The present invention seeks to provide an improved quantum computer. The present invention also seeks to provide a quantum computer in which the qubits are substantially identical to one another and easy to fabricate.
According to the present invention there is provided a quantum computer having at least one qubit comprising a system which exhibits first and second eigenstates, said system being one of a plurality of substantially identical systems and a structure for moveably anchoring said system to a predetermined position.
The system may occur naturally and may comprise a molecule. The molecule may be pyramidal, such as ammonia or cyanamide.
The structure for anchoring the system to the predetermined position may comprise a cage for the system, such as an endohedral molecule. The endohedral molecule may be a buckminsterfullerene molecule, such as a C60 molecule.
The quantum computer may comprise a substrate for anchoring the system thereto. The substrate may include an insulating region, such as silicon dioxide or silicon nitride. The substrate may further include a conducting region, comprising a semiconductor, such as silicon, and may be doped with an impurity. The impurity may be doped to a concentration of at least 1xc3x971018 cmxe2x88x923. The substrate may be patterned.
The quantum computer may include a detector for detecting a state of said system, such as an electrometer. The substrate may be patterned to define the detector.
The system may comprise a system for defining first and second delocalised states, which may have associated with them first and second dipole moments respectively. The first and second dipole moments may be electric dipole moments. The first and second delocalised states may be superpositionable so as to produce said first and second eigenstates. The first and second eigenstates may be split by an energy gap, which can be of the order of 10 xcexceV or greater.
The quantum computer may comprise a further structure for arranging said structure for anchoring said system to said predetermined position, which can be tubular, for example a molecular nanotube and in particular one formed of carbon.
The quantum computer may comprise another qubit which comprises another system substantially identical to said system and another structure for moveably anchoring said another system to another predetermined position. The another structure for moveably anchoring said another system to said another predetermined position may be different from said structure for moveably anchoring said system to said predetermined position.
The quantum computer may comprise a different qubit which comprises a different system which exhibits third and fourth eigenstates, said different system being one of a plurality of substantially identical systems and structure for moveably anchoring said different system to a predetermined position.
According to the present invention there is also provided apparatus including a quantum computer and a source for providing a time dependant electric field to said quantum computer. The source can generate microwaves.
According to the present invention there is also provided apparatus including a quantum computer and control circuitry for controlling said gate electrodes.
According to the present invention there is also provided apparatus including a quantum computer and a refrigerator for cooling said quantum computer.
According to the present invention there is also provided a method of operating the quantum computer comprising applying a first static electric field for causing said first and second eigenstates to resolve into first and second localised states. The method may further comprise measuring said system.
According to the present invention there is also provided a method of operating the quantum computer comprising applying a time-dependent electric field for causing said system to undergo Rabi osciallation.
According to the present invention there is also provided a method of operating the quantum computer comprising applying a second static electric field for altering an energy gap between said first and second eigenstates.
According to the present invention there is also provided a method of fabricating a quantum computer having at least one qubit, the method comprising providing a system which exhibits first and second eigenstates, said system being one of a plurality of substantially identical systems and providing a structure for moveably anchoring said system to a predetermined position.
The method may further comprise moving said system to a specific position.